# Statistical Analysis and Parameter Selection for Mapper

arXiv: https://arxiv.org/abs/1706.00204 · HTML: https://mlsanity.com/paper/1706.00204/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2017.

## Built on by (most cited first, 20 of 20)

- [The Disagreement Problem in Faithfulness Metrics](https://mlsanity.com/paper/2311.07763/) (2023)
- [A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis](https://mlsanity.com/paper/2109.00530/) (2021)
- [Differentiable Mapper For Topological Optimization Of Data Representation](https://mlsanity.com/paper/2402.12854/) (2024)
- [MOUNTAINEER: Topology-Driven Visual Analytics for Comparing Local Explanations](https://mlsanity.com/paper/2406.15613/) (2024)
- [Explainable Mapper: Charting LLM Embedding Spaces Using Perturbation-Based Explanation and Verification Agents](https://mlsanity.com/paper/2507.18607/) (2025)
- [Mapper-type algorithms for complex data and relations](https://mlsanity.com/paper/2109.00831/) (2021)
- [AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm](https://mlsanity.com/paper/2408.06958/) (2024)
- [Topological Interpretability for Deep-Learning](https://mlsanity.com/paper/2305.08642/) (2023)
- [G-Mapper: Learning a Cover in the Mapper Construction](https://mlsanity.com/paper/2309.06634/) (2023)
- [A distribution-guided Mapper algorithm](https://mlsanity.com/paper/2401.12237/) (2024)
- [Topological structure of complex predictions](https://mlsanity.com/paper/2207.14358/) (2022)
- [Improving Mapper's Robustness by Varying Resolution According to Lens-Space Density](https://mlsanity.com/paper/2410.03862/) (2024)
- [Cover Learning for Large-Scale Topology Representation](https://mlsanity.com/paper/2503.09767/) (2025)
- [Topological Data Analysis for Unsupervised Anomaly Detection and Customer Segmentation on Banking Data](https://mlsanity.com/paper/2508.14136/) (2025)
- [Statistical embedding: Beyond principal components](https://mlsanity.com/paper/2106.01858/) (2021)
- [A Mapper Algorithm with implicit intervals and its optimization](https://mlsanity.com/paper/2412.11631/) (2024)
- [Structure-First Point Cloud Learning with Mapper Region Graphs](https://mlsanity.com/paper/2602.05522/) (2026)
- [AMD-FCG: An Enhanced Function Call Graph Dataset with Integrated Topological Features for Malware Detection and Classification](https://mlsanity.com/paper/2606.06815/) (2026)
- [Structured Learning on Mapper Representations](https://mlsanity.com/paper/2608.22044/) (2026)
- [Skeletal Prototypes on Iterative Nerve Expansions](https://mlsanity.com/paper/2609.16170/) (2026)

## Abstract (arXiv)

In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a method to automatically tune its parameters and compute confidence regions on its topological features, such as its loops and flares. This allows to circumvent the issue of testing a large grid of parameters and keeping the most stable ones in the brute-force setting, which is widely used in visualization, clustering and feature selection with the Mapper.